A derivation of conditional cumulants in exponential models

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Let T = (T1, …, Tk, k ≥ 2) be a minimal sufficient statistic for a k-parameter natural exponential model. Consider a partition of T into (T1, T2), where T1 = (T1, …, Tr) and T2 = (Tr+1, …, Tk; 1 ≤ r < k). It is shown that cumulants of the conditional distribution of T1, given T2 = t2, can be computed through the marginal distribution of T2 and the norming constant that makes the model a probability model. The results are illustrated by a few examples.

Original languageEnglish
Pages (from-to)126-129
Number of pages4
JournalAmerican Statistician
Issue number2
StatePublished - May 1994


  • Conditional moments
  • Natural exponential family

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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